Mirror Equation Calculator
Calculate object distance, image distance, focal length, and magnification for spherical mirrors
Spherical Mirror Calculator
Distance from object to mirror pole (negative by convention)
Distance from focal point to mirror pole
Mirror Equation Results
Image Characteristics
Mirror Equation: 1/f = 1/v + 1/u
Magnification: m = -v/u = 0.000
Sign Convention: Cartesian (distances measured from pole)
Cartesian Sign Convention
Concave Mirror
- • f, R: negative
- • u: always negative
- • v: negative (real), positive (virtual)
Convex Mirror
- • f, R: positive
- • u: negative
- • v: positive (virtual)
Plane Mirror
- • f, R: infinity
- • u: negative
- • v: positive, |v| = |u|
Example Problems
Concave Mirror Example
Problem: Object at 30 cm from concave mirror with focal length 20 cm
Given: u = -30 cm, f = -20 cm
Solution:
1/v = 1/f - 1/u = 1/(-20) - 1/(-30) = -1/20 + 1/30 = -1/60
v = -60 cm (real image, inverted)
Magnification = -v/u = -(-60)/(-30) = -2 (enlarged, inverted)
Convex Mirror Example
Problem: Object at 15 cm from convex mirror with focal length 10 cm
Given: u = -15 cm, f = +10 cm
Solution:
1/v = 1/f - 1/u = 1/10 - 1/(-15) = 1/10 + 1/15 = 1/6
v = +6 cm (virtual image, erect, diminished)
Mirror Types
Concave Mirror
Converging mirror, curves inward
- • Can form real and virtual images
- • Used in telescopes, headlights
- • Negative focal length
Convex Mirror
Diverging mirror, curves outward
- • Always forms virtual images
- • Used in car mirrors, security
- • Positive focal length
Plane Mirror
Flat mirror surface
- • Always virtual, erect images
- • Same size as object
- • Infinite focal length
Quick Reference
Mirror Equation
1/f = 1/v + 1/u
Magnification
m = -v/u
Radius Relation
R = 2f
Image Nature
- • Real: v < 0 (concave)
- • Virtual: v > 0
- • Inverted: m < 0
- • Erect: m > 0
Understanding the Mirror Equation
What is the Mirror Equation?
The mirror equation relates the object distance (u), image distance (v), and focal length (f) for spherical mirrors. It's derived from the geometry of light ray paths and the principle that all rays passing through the focal point reflect parallel to the principal axis.
Key Concepts
- •Focal length: Distance from mirror to focal point
- •Object distance: Distance from object to mirror
- •Image distance: Distance from image to mirror
- •Magnification: Ratio of image size to object size
Mathematical Relationships
1/f = 1/v + 1/u
m = -v/u
R = 2f
Applications
- •Telescope and microscope design
- •Automotive mirrors and headlights
- •Solar concentrators and collectors
- •Security and surveillance systems
Sign Convention Rules
Distance Measurements
- • All distances measured from the pole of the mirror
- • Left side of mirror: negative distances
- • Right side of mirror: positive distances
- • Object is always on the left (u is negative)
Image Characteristics
- • Real images: formed on left side (v negative)
- • Virtual images: formed on right side (v positive)
- • Inverted images: negative magnification
- • Erect images: positive magnification